Using the covering number result for sparse vectors (Lemma 3.4 of [1]}), we have
\(\log \mathcal {N}\left(\mathcal {G}(\widehat{r},s);\frac{\sqrt{m}\widehat{r}}{F}\epsilon \right) \le \frac{Cs}{\epsilon ^2}\log \frac{2m}{s}\) 
